Updating Dual Variables in Distributed Optimization using fmincon

Hi there, I am trying to implement a distributed optimization algorithm in MatLab using fmincon and the 'interior-point-algorithm'. I decomposed the overall problem into 3 subproblems, where each subproblem executes one step of the optimization ('MaxIter' in 'optimset' is set to 1) in parallel and communicates with its neighbours afterwards. This is repeated, til the stopping criterion is fullfilled.

Now im reading about the 'interior-point-algorithm' and the update of the dual-variables. And I'm wondering if initial-values for the multipliers and slack-variable are needed, from the last optimization step.

So the question is:

Does the 'interior-point-algorithm' need initial-values for the Lagrange-multipliers and slack-variable?

And if so, is there a possibility to give those as inputs to the 'fmincon'-function?

Hope someone can help me with this.

Thank you!

[Matt J]

I doubt it's possible, but I agree it would be good if it were.

Aside from that, however, your parallelization strategy sounds doubtful. It sounds like it would be better to keep the parallel operations internal to your objective and constraint functions, rather than trying to paralleize execution of fmincon itself.

[Jakob]

I'm doing research on Distributed Optimal Power Flow calculations. So I'm looking for ways to decompose and solve Optimal Power Flow calculations in a distributed way, where each subsystem does one iteration of the optimization and then variables are exchanged. That's why I do parallel optimization and only 1 iteration.

Do you or does anybody have an idea how I could do this, without implementing my own interior-point-method?

I was thinking about including the constraints on my own and do an uncontrained optimization with the additional variables for the multipliers and slack-variables.

[Matt J]

Is there a reason it has to be interior point? Why not try one of the other fmincon algorithms that don't have extra state variables?

[Jakob]

It is a nonlinear problem with nonlinear equality-constraints and bounds as inequality constraints.

It doesnt have to be interior-point, but as it is a large scale problem, I decided to use the default interior-point algorithm.

And all of the algorithms use additional variables. Which have to be updated.

[Scott Weidenkopf]

You mentioned you are reading about the 'interior-point-algorithm'...are you referring to a MathWorks documentation page?

[Jakob]

I was reading literature as well as the MatLab Documentation .

[Scott Weidenkopf]

As of R2017b, providing those initial values is not possible. Warm-starting interior-point methods are an active research area, but it is unclear when that feature will make it into MATLAB.